Definitions:

The greatest common divisor (gcd), of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder.

A general example to help you recognize patterns and spot the information you're looking for

Find gcd (8, 24):

Since the factors of 8 are: 1, 2, 4, 8

and the factors of 24 are: 1, 2, 3, 4, 6, 8, and 12. $$gcd ( 8, 24 ) = 8$$

In real life we use this concept when we try to split things into smaller sections. Trying to figure out how many people we can invite or trying to arrange something in rows or groups.